Cellular algebras and quasi-hereditary algebras: a comparison.
Coalgebra deformations of bialgebras by Harrison cocycles, copairings of Hopf algebras and double crosscoproducts.
Cohomologie de Hochschild des graphes de Kontsevich
Nous calculons la cohomologie de Hochschild directement sur les graphes de Kontsevich. Celle-ci est localisée sur les graphes totalement antisymétriques ayant autant de pieds que de pattes. La considération de cette cohomologie permet de réinterpréter l’équation de formalité pour l’espace .
Cohomologie de Hochschild et espaces projectifs tronqués.
Cohomologies bivariantes de type cyclique
In the article we propose a construction of bivariant cohomology of a couple of chain complexes with periodicities. In this way we obtain definitions of bivariant dihedral and bivariant reflective cohomology of an algebra . Bivariant cyclic and quaternionic cohomologies appear as particular cases of this construction. The case of invertible in the ground ring is studied particulary.Dans cet article nous proposons une définition de la cohomologie bivariante pour une paire de complexes de chaînes...
Cohomology Groups of Infinite Dimensional Algebras.
Cohomology groups of reduced enveloping algebras.
Cohomology of algebras of dihedral type. I.
Cohomology of algebras of semidihedral type. IV.
Cohomology of some graded differential algebras
We study cohomology algebras of graded differential algebras which are models for Hochschild homology of some classes of topological spaces (e.g. homogeneous spaces of compact Lie groups). Explicit formulae are obtained. Some applications to cyclic homology are given.
Cohomology of the triangular algebra and applications. (Cohomologie de l'algèbre triangulaire et applications.)
Cohomology ring of n-Lie algebras.
Natural graded Lie brackets on the space of cochains of n-Leibniz and n-Lie algebras are introduced. It turns out that these brackets agree under the natural embedding introduced by Gautheron. Moreover, n-Leibniz and n-Lie algebras turn to be canonical structures for these brackets in a similar way in which associative algebras (respectively, Lie algebras) are canonical structures for the Gerstenhaber bracket (respectively, Nijenhuis-Richardson bracket).
Commutative diagrams for the inflation-restriction sequence
Complexes de Koszul quantiques
Nous construisons des généralisations des complexes de Koszul, associées à des symétries vérifiant l’équation de Yang-Baxter. Certains de ces complexes sont acycliques et permettent de calculer l’homologie de Hochschild et cyclique de déformations quantiques d’algèbres symétriques et extérieures. Nous donnons des résultats précis pour l’espace affine quantique multiparamétré. Il est également possible de définir des complexes de Koszul pour des algèbres enveloppantes et de Sridharan d’algèbres de...
Complexity and periodicity
Let M be a finitely generated module over an Artin algebra. By considering the lengths of the modules in the minimal projective resolution of M, we obtain the Betti sequence of M. This sequence must be bounded if M is eventually periodic, but the converse fails to hold in general. We give conditions under which it holds, using techniques from Hochschild cohomology. We also provide a result which under certain conditions guarantees the existence of periodic modules. Finally, we study the case when...
Construction géométrique des idempotents eulériens. Filtration des groupes de polytopes et des groupes d'homologie de Hochschild
Cyclic cohomology of certain nuclear Fréchet algebras and DF algebras
We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain -algebras. We use well-developed homological techniques together with some niceties of the theory of locally convex spaces to generalize the results known in the case of Banach algebras and their inverse limits to wider classes of topological algebras. To this end we show that, for a continuous morphism ϕ: x → y of complexes of complete nuclear DF-spaces, the isomorphism of cohomology groups H...
Cyclic cohomology of (extended) Hopf algebras
We review recent progress in the study of cyclic cohomology of Hopf algebras, extended Hopf algebras, invariant cyclic homology, and Hopf-cyclic homology with coefficients, starting with the pioneering work of Connes-Moscovici.
Cyclic homology, a survey
Cyclic homology and equivariant homology.